From the connection string? Not that I'm aware of.
Unmanaged (standard) ODP.net can set a TNS path as an environment variable, or in the registry. See this for some more info: http://www.dba-oracle.com/t_windows_tnsnames.ora_file_location.htm
The managed beta has a web.config/app.config setting that lets you set the path, which is quite handy.
<add name="ORAConnectionString" connectionString="Data Source=MyTNSnames;User ID=MyUser;Password=MyPassword;" providerName="System.Data.OracleClient"/>
This connection string looks ok. Just put in your data source your TNS name. Does it give any error?
Use the fancy new app/web.config method using 12c fully managed provider. It's very nice:
EDIT: forgot to add this.. it has to be right after <configuration> on line 2
<section name="oracle.manageddataaccess.client" type="OracleInternal.Common.ODPMSectionHandler, Oracle.ManagedDataAccess" />
<section name="log4net" type="log4net.Config.Log4NetConfigurationSectionHandler, log4net" />
<setting name="TraceLevel" value="0" />
<setting name="TraceOption" value="0" />
<setting name="TraceFileLocation" value=".\logs" />
<dataSource alias="orcldb1.blahblah.com" descriptor="(DESCRIPTION=(ADDRESS_LIST=(FAILOVER=on)(ADDRESS=(PROTOCOL=TCP)(HOST=host1.blahblah.com)(PORT=1521))(ADDRESS=(PROTOCOL=TCP)(HOST=host2.blahblah.com)(PORT=1521))(ADDRESS=(PROTOCOL=TCP)(HOST=host3.blahblah.com)(PORT=1521))(ADDRESS=(PROTOCOL=TCP)(HOST=host4.blahblah.com)(PORT=1521)))(CONNECT_DATA=(FAILOVER_MODE=(TYPE=select)(METHOD=basic)(DELAY=50))(SERVER=default)(SERVICE_NAME=MY_AWESOME_SERVICE)))"/>
<add name="MyOracleDBString" connectionString="user id=oracleuser;password=secret;data source=orcldb1.blahblah.com"/>
And you can of course encrypt the connectionStrings part which has your credentials, while still knowing what your "TNS" looks like. Managed provider checks this before looking for existing TNS files.
The new Managed provider in 12c is like discovering the wheel for us .NET folks.
Also, to answer your original question, the answer is yes. You need to edit the MACHINE.CONFIG file ( c:\Windows\Microsoft.Net\Framework\[Version]\Config\machine.config ). Mine, on my local developer workstation, looks like this:
<setting name="tns_admin" value="c:\oracle\tns" />
I always have ORACLE_BASE setup as c:\oracle with one folder \tns that contains my tnsnames instead of using one within each provider. it seems dumb to have 5 tnsnames.ora files if you have 5 clients installed (not that I have 5 clients installed....)